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Two dice wheel: totals from 2 to 12

This wheel does not treat 2 and 7 the same, because a pair of dice does not. Each total carries a weight equal to the number of ways two dice can make it.

SpacespinCtrl+Enterspin while typingFfull screen

One entry per line. Add *3 after a name to give it three times the chance.

Roll two dice

2

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    Why 7 comes up most

    Two dice can land in 6 × 6 = 36 equally likely ways. A total of 2 needs both dice to show 1, which is one way. A total of 7 can be 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2 or 6 + 1: six ways. The weights on the wheel (“7 *6”, “2 *1”) copy those counts, so the wheel gives the same odds as rolling a real pair.

    TotalWaysChance
    212.8%
    325.6%
    438.3%
    5411.1%
    6513.9%
    7616.7%
    8513.9%
    9411.1%
    1038.3%
    1125.6%
    1212.8%

    A probability lesson in 20 minutes

    1. Ask the class to predict which total will win most often. Plenty of students say every total is equal.
    2. Spin 50 times in Full screen, with a different student pressing Space each time.
    3. Open the Results tab and tally the totals on the board as a bar chart.
    4. Compare it with the table above. The tally will be lumpy, but the middle totals will beat the ends. Talk about why 50 trials is not enough for a smooth curve.

    Use it for board games

    Any game that only cares about the sum of two dice works with this wheel: resource-trading games, racing games, classroom board games. If your game has rules for doubles (roll again, get out of a penalty square), you need to see each die separately: use the dice roller with two dice, or spin the single dice wheel twice.

    Questions and answers

    Why not just put 2 to 12 on the wheel with no weights?

    That would make 12 as likely as 7, which is not how dice behave. Games built around two dice, especially ones where 7 is special, would feel wrong. The weights fix that.

    What are the “*6” and “*1” in the entry box?

    They are weights. “7 *6” means 7 has six chances for every one chance of “2 *1”. Delete the weights and every total becomes equally likely.

    Can I get a doubles result?

    Not from this wheel, because it only knows the total. A 6 could be 3 + 3 or 1 + 5. For doubles, roll two separate dice.

    Tools that go with it

    More in Numbers and letters

    Number and letter wheels (13 wheels) →

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